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  4. A man can swim with speed 5ms- 1 in still river while the river is also flowing with speed 10ms- 1 . If the width of the river is 100m then minimum possible drift is

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Q. A man can swim with speed $5ms^{- 1}$ in still river while the river is also flowing with speed $10ms^{- 1}$ . If the width of the river is $100m$ then minimum possible drift is

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

Solution
Let the man swim with an angle $\theta $ with upstream , By using the concept of relative velocity with respect to river and substituting given values,
$Drift=\left(10 - 5 cos \theta \right)\frac{100}{5 sin ⁡ \theta }$
Differentiate this find $\theta $ at extremum & then put $\theta $ value in the formula
Drift $=100\sqrt{3} \, m$ .